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C5×C11×Dic6 #13050406

order1320
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic6
unambiguous semidirect productC3⋊(C5×Q8×C11)

Splittings

HallC3×C5×C11 ⋊ Q8
HallC3×C11 ⋊ C5×Q8
HallC3×C5 ⋊ Q8×C11
SylowC3 ⋊ C5×Q8×C11

Subgroups

subgroupG/H
centerC2×C5×C11C2×D3
commutator, cosocleC2×C3C22×C5×C11
FrattiniC2C2×C5×D3×C11
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C22
hypercenterC4×C5×C11D3
hypocenterC3C5×Q8×C11
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C11 ◁ C4×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1320

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20)(21,24,23,22)(25,26,27);(17,21,19,23)(18,22,20,24)(26,27)

Conjugacy classes & character table

495 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 110);